Broadband semiconductor faraday effect devices in the infrared

ABSTRACT

A Faraday rotator is formed of a class of semiconductor materials of low free carrier density wherein, in the presence of a suitable magnetic field, interband transition Faraday rotation is opposite in sign from free carrier effect Faraday rotation and interband transition Faraday rotation predominates over free carrier effect Faraday rotation such that net Faraday rotation can remain nearly unchanged over broad IR spectral regions where the short wavelength limit is typically near the bandgap absorption. Thus, the class of semiconductors meeting these conditions can function as high performance broadband optical isolators in the infrared. Suitable materials include InAs of suitable purity.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims benefit under 35 U.S.C. §119 to U.S. ProvisionalPatent Application Ser. No. 61/727,494 filed Nov. 16, 2012, which isincorporated herein for all purposes.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH AND DEVELOPMENT

Not Applicable

REFERENCE TO A “SEQUENCE LISTING,” A TABLE, OR A COMPUTER PROGRAMLISTING APPENDIX SUBMITTED ON A COMPACT DISK

Not Applicable

BACKGROUND OF THE INVENTION

This invention relates generally to broadband Faraday effect devicessuch as optical isolators for use with lasers in the infrared spectralregion. The invention is useful with quantum cascade laser diodes,quantum cascade laser diode arrays, fiber lasers with or withoutnonlinear frequency conversion, CO₂ and other infrared gas lasers, orany type of infrared laser source having broadband gain which issensitive to optical feedback.

Most materials have a rich spectroscopic fingerprint in the infrared.This has resulted in a high level of interest in broadly tunable lasersources such as quantum cascade diode lasers in this wavelength region.Typical applications for quantum cascade diode lasers are exemplified bylaboratory and remote environmental sensing of harmful materials andgases using various spectroscopic techniques. For remote sensingapplications, the power levels available can be increased by amplifyingquantum cascade diode lasers directly with solid state or fiber laserbroadband amplifiers or by broadband nonlinear frequency extensionmethods pumped by solid state and fiber lasers. CO₂ lasers are anotherexample of lasers which have gain over broad wavelength ranges in theinfrared. Using CO₂ laser systems based upon feedback sensitive CO₂laser oscillators followed by CO₂ power amplifiers to efficiently makeplasmas necessary for extreme ultra-violet generation at 13.5 nm iscurrently envisioned as an enabling technology for future compact andenergy efficient semiconductor devices. All of these applicationsbenefit from 100% coupling between the laser source and respectiveapplication target. Many of the laser sources named above are verysensitive to optical feedback. Hence minimizing optical feedback intothe laser cavity is important for laser stability and/or preventingdamage of laser components. In waveguide lasers such as quantum cascadediode lasers, the return radiation can couple into the laser creatingmodal instability and resulting frequency instability and/or opticaldamage of diode laser facets. In more powerful laser systems, such asthe CO₂ laser system for EUV described above, a weak reflected pulse oflight traveling in the reverse direction may get amplified in theamplifier section(s) of the laser and cause damage to the oscillator orotherwise cause the CO₂ laser oscillator to become unstable.

Optical isolators are routinely used to decouple a laser oscillator fromdownstream laser amplifier noise radiation and/or target reflections.Optical isolators use Faraday effect rotation by using a magneto-opticalmaterial in a strong magnetic field co-axial with the laser radiation torotate the plane of polarization 45°. Surrounding the Faraday rotator bypolarizers aligned with the input and output linear polarization statescompletes the optical isolator. Because Faraday effect rotation isnon-reciprocal (i.e. the sense of rotation does not depend upon thedirection of propagation), any backward propagating radiation will havethe plane of linear polarization rotated a further 45° resulting in apolarization state which is 90° to the transmission axis of the inputpolarizer—where it will consequently experience high backwardtransmission loss. This reverse radiation loss is typically on the orderof 30 dB for single stage optical isolators.

The magnitude of Faraday rotation in magneto-optic materials used inoptical isolators normally has wavelength dependence or dispersion. As aresult, an optical isolator will typically only have high isolation at aspecific wavelength. Techniques have been developed to compensate forthe normal Faraday rotation dispersion of magneto-optic materials. Manyof these techniques have relied upon the wavelength dispersion ofoptical rotators and/or waveplates to compensate for the Faradayrotation dispersion in the isolation direction in the visible and nearinfrared spectral regions [U.S. Pat. No. 4,712,880, December 1987,Shirasaki, M., “Polarization rotation compensator and optical isolatorusing the same”; and P. A. Schulz “Wavelength independent Faradayisolator”, Appl. Opt. 28, 4458-4464 (1989)]. However, because theavailable materials (and consequently available dispersion) of opticalrotators and waveplates are limited in the infrared, this technique hasnot yet resulted in commercially viable broadband optical isolators inthe infrared. Further, although this method can give broadband isolationin the visible and near infrared, all dispersions add in the forwardtransmitting direction. This leads to reduced transmission away from acentral design wavelength relative to conventional narrow band opticalisolators. In the 1.55 μm band used for telecommunications, namely, from1.5 μm to 1.62 μm, iron garnets have been doped with various rare earthelements to achieve nearly flat Faraday rotation over broad wavelengthranges [Z. C. Xu, M. Huang and M. Li, “A compounded rare-earth irongarnet single crystal exhibiting stable Faraday rotation againstwavelength and temperature variation in the 1.55 μm band,” J. Magnetismand Magnetic Materials 307 (2006) 74-76]. These efforts have not beenapplied to longer wavelengths due in part to the fact that currentlyknown garnets become opaque above 6 μm [D. L. Wood and J. P. Remeika,“Effect of impurities on the optical properties of yttrium iron garnet,”J. Appl. Phys. 38, 1038-1045 (1967)]. There have been some efforts andreports citing large Faraday rotation in semiconductors due to freecarrier effects with reasonable transmission over a wide range ofinfrared wavelengths. The performance of these materials has shown themost promise however only with cryogenic cooling [A. V. Starobor, D. S.Zheleznov, O. V. Palashov, and E. A. Khazanov,” Magnetoactive media forcryogenic Faraday isolators,” J. Opt. Soc. Am. B 28, 1409-1415 (2011)and W. T. Boord and Y. H. Pao and F. W. Phelps and P. C. Claspy,“Far-infrared radiation isolator,” IEEE J. Quantum Electron. 10, 273-279(1974)]. To date, no infrared broadband optical isolation or infraredbroadband optical isolator has been reported.

The following is background information that describes the Faradayeffect. The Faraday effect is a fundamental physics phenomenon whereinthe plane of polarization of linearly polarized light is rotated aboutthe propagation axes in a magneto-optical medium which is magnetizedparallel to the direction of light propagation. A magneto-opticalmaterial under external magnetic field exhibits different phasevelocities for right and left circularly polarized light. The amount ofspecific polarization rotation (rotation per unit length) is given by:

θ=½k ₀(n ⁻ −n ₊),

where k₀ is the vacuum propagation wave vector, n₊(n⁻) is the refractiveindex for right (left) circular polarized light. The different phasevelocities for right and left circularly polarized light result inrotation of a linear polarization θ, known as Faraday rotation, whenlight propagates through a magneto-optic material of length L in thepresence of a magnetic field B in the direction of propagation theresulting polarization rotation angle is commonly expressed as:

θ=V×B×L

Where the Verdet constant V quantifies how efficiently the magneto-opticmaterial will perform as a Faraday rotator. Unlike polarization inoptical rotators (such as quartz), Faraday rotation θ isnon-reciprocal—the sense of rotation is independent of the direction oflight through the magneto-optic medium.

Faraday rotation in semiconductor materials has been observed for manyyears [B. Lax and Y. Nishina “Interband Faraday Rotation in III-VCompounds,” J. Appl. Phys. 32, 2128 (1961)]. At photon energies far froma bandgap, this Faraday rotation was known to predominantly result fromfree carrier effects with some minor additional Faraday rotation,particularly at low free carrier density, also attributed to interband(bound carrier) transitions. Near an absorptive bandgap, Faradayrotation due to interband transitions is known to become very large butunusable because the semiconductor material becomes opaque. In somesemiconductors, including InAs, these two effects have been known tohave opposite sign of polarization rotation [M. Cardona, “Electroneffective masses of InAs and GaAs as a function of temperature anddoping,” Phys. Rev. 121, 752-758 (1961)]. The presence of two competingFaraday rotation mechanisms, interband transitions and free carriereffects, together with unpredictable free carrier density due toimpurities, has complicated the design of an isolator based onsemiconductors materials.

Faraday rotation contributions due to the free carrier effect make thedevice highly dependent on the type of, amount of, and uniformity of thedoping. A small variation in Faraday rotation in the isolator crystalwill show a limiting extinction of:

$10{\log \left( {\frac{\pi}{4}\frac{\Delta\theta}{\theta}} \right)}^{2}$

For example, only 10 percent variation in doping material in asemiconductor corresponds to 10 percent variation in Faraday rotation,and according to the above relation it gives about 22 dB extinctionlimit. It can be difficult to dope semiconductors crystals to suchdoping level tolerances. For example, because dopants are notpreferentially incorporated into the crystal lattice in Czochralskigrowth of semiconductor crystals such as InAs, the dopant level istypically twice as high near the seed end relative to the dopantconcentration at the tail end of a growth boule [InAs dopantspecifications from InAs data sheet, Wafer Technology LTD, MiltonKeynes, UK, www.wafertech.co.uk]. This large amount of dopingnon-uniformity makes it difficult to consistently produce practicaloptical isolator products based upon doped semiconductors.

Historically, undoped semiconductors such as InAs have also hadvariations in free carrier density due to difficulties in controllingimpurity levels in early effort semiconductor crystal growth. This gaveconflicting and unpredictable results regarding the contributions toFaraday rotation from interband transitions versus free carrier effectsin pioneering research [E. D. Palik, S. Teitler, and R. F. Wallis, “Freecarrier cyclotron resonance, Faraday rotation, and voigt doublerefraction in compound semiconductors,” J. Appl. Phys. 32, 2132 (1961)].For this reason, and because of the large increase in Faraday rotationaway from the bandgap achievable with higher free carrier density, mostknown studies of Faraday rotation in semiconductor materials havefocused upon doped substrates where the free carrier density is largeand predominant over any Faraday rotation due to interband transitions.

What is needed is an efficient room-temperature broadband Faradayrotator operative in the infrared suitable for use in Faraday effectdevices such as optical isolators and circulators.

SUMMARY OF THE INVENTION

In accordance with this invention, a Faraday rotator for use in Faradayrotation applications is formed of a class of semiconductor materials ofa low free carrier density wherein, in the presence of a suitablemagnetic field, interband transition-type Faraday rotation is oppositein sign from free carrier effect-type Faraday rotation and whereininterband transition-type Faraday rotation predominates over freecarrier effect-type Faraday rotation such that net Faraday rotation isnearly independent of frequency and can remain nearly unchanged overbroad IR spectral regions where the short wavelength limit is typicallynear the bandgap absorption. This class of semiconductor materials is adeparture from known prior art employed to achieve Faraday rotation inthe infrared. Thus, the class of semiconductor materials meeting theseconditions can function as high performance broadband optical isolatorsin the infrared spectral region.

In a specific embodiment of the invention the low free carrier densitysemiconductor is undoped Indium Arsenide (InAs) with a direct bandgapenergy=0.345 eV corresponding to 3.55 μm. Near the bandgap at 3.55 μm,interband transition-type Faraday rotation dominates free carriereffect-type Faraday rotation. Indium arsenide meets the criterion ofhaving opposite sign Faraday rotation due to interband transitions andfree carrier effects. In addition, it has a wide bandgap that thermallyinduced carrier concentration at room temperature has insignificantinfluence on free carrier concentration. This enables broadband Faradayrotation suitable for use in a broadband isolator extending from 4 μm to7 μm in the mid-infrared.

The broadband infrared Faraday rotation of this invention is applicablein any commonly used device which is based upon Faraday effect rotationsuch as optical isolators, optical circulators and Faraday mirrors. Theoptical isolators and optical circulators may be either polarizationmaintaining (PM) or polarization independent (PI) by any of the meanscommonly known in the art. Faraday effect rotation in accordance withthe invention may be used in any of the commonly used configurationssuch as rod and slab shapes and/or multipass or thin-disk designs.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a depiction of a generic Faraday rotator device according tothe invention.

FIG. 2 is a plot fitting Faraday rotation data at 4.55, 7.5 and 10.6 μmto a theoretical curve based upon interband transitions and free carriereffects.

FIG. 3 is a plot of the magnet field profile used in the preferredembodiment.

FIG. 4 is a plot of the transmission spectrum for 1 mm thick undopedInAs wafer with a free carrier density of N=2.5×10¹⁶ cm⁻³.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates a generic Faraday rotator 10 incorporating asemiconductor material 12 in accordance with the invention. The rotator10 includes an optical input port 14 and an optical output port 16 withan optical path 18 therebetween. A magnet 20 is provided to provide amagnetic field along the optical path 18. The semiconductor material 12according to the invention is disposed along the optical path 18 and hasthe characteristics as herein described, namely, in the presence of asuitable magnetic field, interband transition-type Faraday rotation isopposite in sign from free carrier effect-type Faraday rotation andinterband transition Faraday rotation predominates over free carriereffect Faraday rotation such that net Faraday rotation can remain nearlyunchanged over broad IR spectral regions where the short wavelengthlimit is typically near the bandgap absorption.

FIG. 2 shows a plot of an effect useful according to the invention butheretofore unexploited. According to the invention, it has beendiscovered that undoped InAs semiconductor substrate materials with aspecified low free carrier density of less than about 3.0×10¹⁶ cm⁻³ andmore specifically between about 2.0×10¹⁶ cm⁻³ and 2.5×10¹⁶ cm⁻³ has

Faraday rotation and optical absorption characteristics nearlyindependent of wavelength in the mid-IR range of 4 μm to 7 μm. Unlikemany historical results where Faraday rotation was dominated by freecarriers due to impurities or intentional doping, Faraday rotation inundoped InAs near the bandgap at 4 μm predominates due to contributionsfrom the interband transitions in the aforementioned wavelength rangewith a relatively minor contribution from the low free carrier density.Although the Faraday rotation attributable to interband transitions isthe dominant effect at low free carrier density near the bandgap, theresidual free carrier density gives Faraday rotation of opposite signand sufficient magnitude and dispersion to substantially compensate thedispersion of the interband transition Faraday rotation. Thissuperposition of these two contributions to Faraday rotation in theundoped InAs wafers notably results in substantially flat Faradayrotation across the spectral range of 4 to 7 μm. This is the phenomenonshown in FIG. 2. The polarization rotation due to interband transitionsis determined by crystal structure and is largely independent of thefree carrier density. Using modern crystal growth methods and highpurity melt precursors, impurity levels can be well controlled enablingpredictable Faraday rotation resulting from interband transitions andresidual free carrier Faraday rotation. From data about undoped InAsindicating that the free carrier density from the seed end to the tailend of the growth boule did not vary by more than 5% it can be confirmedthat free carrier density can be much better in undoped samples than indoped samples.

The limits of applicability of the invention can be theoreticallyunderstood. Referring to FIG. 2, below the InAs bandgap corresponding to3.55 μm the negative Faraday rotation is shown to increase dramaticallyas expected due to interband transitions. The FTIR spectrum of InAsshown in FIG. 4 confirms this significant absorption near the bandgapbelow 4 μm. At wavelengths above 7.5 μm, the Faraday rotation of InAsshows a linear relationship with the square of wavelength; acharacteristic feature of the dominant free carrier effect polarizationrotation. However, at shorter wavelengths approaching the bandgap energy(below 7 μm) this linear behavior is no longer valid [M. Cardona,“Electron effective masses of InAs and GaAs as a function of temperatureand doping,”, Phys. Rev. 121, 752-758 (1961)]. As the bandgap energy isapproached Faraday rotation becomes increasingly due to interbandtransitions, and in the case of InAs, it is in the opposite direction offree carrier polarization rotation.

In the case of free carrier Faraday rotation a semi-classical modelgives the polarization rotation of a semiconductor wafer of thickness Lin a magnetic field B as

θ=V×B×L

where the Verdet constant is given by:

$V = {\frac{\mu_{o}N\; q^{3}\lambda^{2}}{8\pi^{2}n\; m^{*2}c}.}$

The absorption coefficient is:

${\alpha = \frac{\mu_{o}N\; q^{2}\lambda^{2}}{4\pi^{2}n\; m^{*}c\; \tau}},$

where n is the material refractive index, m* is the carrier effectivemass, N is the carrier density, τ is the effective carrier relaxationtime, λ is the laser wavelength, c is the speed of light in vacuum, q iselectronic charge, and μ₀ is the permeability of free space. The aboveequations for free carrier Faraday rotation are valid only if thefollowing parameter conditions are satisfied:

ω_(r)

ω_(c)

ω≦ω_(p)

nω,

where ω_(r) is the effective carrier relaxation frequency, ω_(c) is thecyclotron frequency, ω is the laser frequency, and ω_(p) is the plasmafrequency.

In experiments leading to this invention, an undoped InAs wafer waschosen that had residual electron carrier density specified as 2.5×10¹⁶cm⁻³. The effective mass of free carrier is reported as 0.027 m_(e) andeffective carrier relaxation time is about 1.4×10⁻¹² sec. These valuesgive the results of ω_(r)=0.69 THz, ω_(c)=6.47 THz, and ω_(p)=54.28 THz.However, in the wavelength range of 4 μm to 7 μm, the respective laserfrequencies are ω=471.2 THz to 269.2 THz. Consequently an undoped InAswafer cannot satisfy the free carrier parameter inequality conditiongiven above because the laser frequency ω is always substantiallygreater than the plasma frequency ω_(p). Here it can safely be assumedthat the Faraday rotation results primarily from interband transitionsof undoped InAs.

Some semiconductors including specifically InAs show an opposite sign ofFaraday rotation due to interband transitions relative to Faradayrotation due to the free carrier effect. The actual reason is a matterof ongoing research. In FIG. 2 the theoretical Faraday rotation frominterband transitions and free carrier effects were summed and fitted tothe three experimental points for the InAs sample. At longer wavelengthsthe Faraday rotation approaches a linear relationship with the square ofwavelength, signifying free carrier effect Faraday rotation as expected.Whereas, at shorter wavelengths, this relationship does not apply, andthere is a region with balancing between two effects, which results inwavelength stable magneto-optical activity. In the present case, withthe choice of InAs with the optimal free carrier density of about2.5×10¹⁶ cm⁻³, the polarization rotation approaches a stable state inthe wavelength range of at least 4 μm to 7 μm, evidently due to thebalancing of contributions from the two oppositely signed Faradayrotation effects. The short wavelength limit is due to the 0.345 eV bandgap energy corresponding to a wavelength of 3.55 μm. However, theoptimal free carrier density is temperature dependent and is given by

N∝T^(8/2) ^((μ-E) ^(g) ^()/2k) ^(B) ^(T)

where E_(g) is the bandgap energy, μ is the Fermi level, and k_(B) isthe Boltzmann constant. Therefore, the optimal carrier density would belower at lower temperatures. The optimal carrier density at zero degCelsius would be down to around 1.5×10¹⁶ cm⁻³ from 2. 5×10¹⁶ cm⁻³.

Two sets of InAs wafers of different thicknesses and low free carrierdensity were investigated. A 1-mm thick, double-side polished undopedInAs sample from a 2-inch wafer from El-Cat [El-Cat Inc, 160 Hopper Ave,Waldwick, N.J. 07463, USA] cut into 10×10 mm square plates, served asSet One. The carrier density of the plate is 2.5×10¹⁶ cm⁻³, as measuredby the Hall effect, and the mobility as supplied by the vendor is 22,000cm/Vs. A high purity undoped InAs 2-inch, 0.5 mm thick, double-sidepolished sample from Wafer Technology of Milton Keynes, UK, also cutinto 10×10 mm square plates served as Set Two. The carrier densitymeasured as 2.0×10¹⁶ cm⁻³, and the mobility is 22,500 cm/Vs as measuredby the manufacturer.

The InAs plates were sandwiched between two hollow aluminum holders in acopper tube to adjust the wafer position inside a magnet assembly. Anon-optimized magnet assembly was used to produce a magnetic field up to1.27 Torr in the center of the magnet. The magnetic profile is given inFIG. 3. The transmission spectrum (uncorrected for Fresnel reflectionloss of the uncoated wafer) of the set one plate by FTIR spectroscopy ispresented in FIG. 4. The transmission spectrum of InAs shows a ratherflat curve in a wide range of wavelengths from 4 μm to 9 μm. MeasuredFaraday rotation of InAs at two wavelengths was obtained using quantumcascade lasers, one operating at 4.55 μm and the other one at 7.5 μm.Set One had a Verdet constant of 6.7 deg/mm-T and 6.9 deg/mm-T at 4.55μm and 7.5 μm wavelengths, respectively, whereas Set Two shows a Verdetconstant as 7.0 deg/mm-T at both of the above-listed wavelengths withquantum cascade laser diodes. A Verdet constant was measured at 10.6 μmof 13.8°/mm-T for both sample sets. In all experiments there was about a10 percent error in measurement. With a magnet assembly optimized forthis application, a 2 T magnetic field strength over a 3.2 mm lengthcould easily be reached, which results in over 90% wafer transmissionover a broad band of wavelengths for 45° polarization rotation. Theisolation ratio for both samples was 24 dB which is relatively high foruncoated samples. Isolation can be expected to exceed 30 dB withbroadband anti-reflection coated InAs wafers.

In accordance with the invention, low free carrier density undoped InAsexhibits stable Faraday rotation in the broad band mid-IR wavelength of4 μm to 7 μm. Recent developments and improvements in InAs wafer qualitypermits one to take advantage of the interband transition Faradayrotation near the bandgap of low free carrier density semiconductors tomake practical Faraday rotators for such applications as broadbandoptical isolators. InAs wafers now readily available from respectedsemiconductor vendors, together with high performance permanent magnetassemblies and recently released high quality wire grid polarizers fromMoxtek [Moxtek, Inc., 452 W 1260 N, Orem, Utah 84057, USA] with betterthan 98% transmission and 30 dB extinction in the mid-infrared enablehigh performance broadband mid-IR optical isolators. These low freecarrier density InAs based broadband mid-IR optical isolators aresuitable for use with application specific discrete wavelength lasers ortunable mid-IR laser sources suitable for a wide range of applicationsand devices operative in the mid-IR from 4 μm to 7 μm.

The broadband infrared Faraday rotation of this invention is applicableas is generally known in the art to any commonly used optical devicewhich is based upon Faraday effect rotation such as optical isolators,optical circulators and Faraday mirrors. The optical isolators andoptical circulators may be either polarization-maintaining (PM) orpolarization-independent (PI) by any of the means commonly known in theart. Faraday effect rotation in accordance with the invention may beused in accordance with the known art in any commonly usedconfigurations such as rod and slab shapes and/or multipass or thin diskdesigns.

The invention has been explained with respect to specific embodiments.Other embodiments will be evident to those of ordinary skill in the art.Therefore, it is not intended that this invention be limited, except asindicated by the appended claims.

What is claimed is:
 1. A broadband infrared Faraday rotator comprising:an optical input port; an optical output port; a semiconductor materialdisposed along a light path between the optical input port and theoptical output port, said semiconductor material having low free carrierdensity and capable of Faraday rotation of a sign due to interbandtransitions opposite of free carrier effects, said Faraday rotation dueto said interband transitions and said free carrier effects resulting instable net Faraday rotation over a broad infrared wavelength range; anda magnet providing a magnetic field coaxial with the optical path and ofsufficient strength to induce at least 45 degrees of Faraday rotation ofthe semiconductor material.
 2. The Faraday rotator of claim 1 whereinsaid low free carrier density is sufficiently low that said Faradayrotation due to said interband transitions is predominant as a source atthe short wavelength limit near the bandgap of said stable net Faradayrotation over broad infrared wavelength range.
 3. The Faraday rotator ofclaim 1 wherein said semiconductor material is undoped.
 4. The Faradayrotator of claim 1 wherein said semiconductor material is IndiumArsenide (InAs).
 5. The Faraday rotator of claim 4 wherein said IndiumArsenide semiconductor material has a free carrier density of less thanabout 3×10¹⁶ cm⁻³ at room temperature such that the Indium Arsenidesemiconductor material has Faraday rotation and optical absorptioncharacteristics nearly independent of wavelength in the mid-IR range. 6.The Faraday rotator of claim 4 wherein said Indium Arsenidesemiconductor material has a free carrier density in the range of 2×10¹⁶cm⁻³ to 3×10¹⁶ cm⁻³ at room temperature and said stable net Faradayrotation over said infrared wavelength range is inclusive of thewavelengths between 4 μm and 7 μm.
 7. The Faraday rotator of claim 1configured to form an element of a broadband Faraday effect devicesuitable for use in at least one of an optical isolator, a Faradaymirror, and an optical circulator.
 8. A broadband infrared Faradayrotator comprising: an optical input port; an optical output port; asemiconductor material disposed along a light path between the opticalinput port and the optical output port, said semiconductor materialhaving low free carrier density and capable of Faraday rotation of asign due to interband transitions opposite of free carrier effects, saidFaraday rotation due to said interband transitions and said free carriereffects resulting in stable net Faraday rotation over a broad infraredwavelength range; a magnet providing a magnetic field coaxial with theoptical path and of sufficient strength to induce at least 45 degrees ofFaraday rotation of the semiconductor material. wherein the Faradayrotation 0 of the semiconductor wafer of thickness L in the magneticfield B due to free carrier effect is given by:θ=V×B×L the Verdet constant V being given by:$V = {\frac{\mu_{o}N\; q^{3}\lambda^{2}}{8\pi^{2}n\; m^{*2}c}.}$wherein the semiconductor material has an absorption coefficient givenby:${\alpha = \frac{\mu_{o}N\; q^{2}\lambda^{2}}{4\pi^{2}n\; m^{*}c\; \tau}},$where n is the material refractive index, m* is the carrier effectivemass, N is the carrier density, τ is the effective carrier relaxationtime, λ is the laser wavelength, c is the speed of light in vacuum, andμ₀ is the permeability of free space, for laser frequencies satisfyingthe relation:ω_(r)

ω_(c)

ω≦ω_(p)

nω, where ω_(r) is the effective carrier relaxation frequency, ω_(c) isthe cyclotron frequency, ω is the laser frequency, and ω_(p) is theplasma frequency.
 9. An optical isolator incorporating a broadbandinfrared Faraday rotator comprising: an optical input port; an opticaloutput port; a semiconductor material disposed along a light pathbetween the optical input port and the optical output port, saidsemiconductor material having low free carrier density and capable ofFaraday rotation of a sign due to interband transitions opposite of freecarrier effects, said Faraday rotation due to said interband transitionsand said free carrier effects resulting in stable net Faraday rotationover a broad infrared wavelength range; a magnet providing a magneticfield coaxial with the optical path and of sufficient strength to induceat least 45 degrees of Faraday rotation of the semiconductor material; afirst polarizer between the optical input port and the semiconductormaterial: and a second polarizer between the optical output port and thesemiconductor material.